## solve second order ode ...

Hi

We solve the following ode in the interval (0,Pi):

diff(u(x),x,x)+u(x)=f(x);

bcs=u(0)=0, u(Pi)=0;

Stating one example of many conditions for such equation to have a
valid solution

Many thanks

## Second order ODE with infinity condition...

I got a problem with solving a second order ODE.

The ODE is :

-V(xi)+(1/2)*xi*(diff(V(xi), xi))+(1/4)*(diff(V(xi), xi, xi))=-(1/2)*k2*(diff(H(xi), xi))-k1*n*X/E+1+k2

where k1,k2,n,X,E  all are constant.

the condition is :

V(xi) tends to 2*xi^2 as xi tends to infinity.

I used 'dsolve' to solve the equation firstly, and got a solution with two constant C1 and C2, I want to use the condition to elimilate C2, so I used limit(sol,xi=infinity)=2*xi^2. But when I used the command 'limit', I can't get the answer.

Could any one help me?

Many thanks!!!

## convert second order ode to first order ode.......

Hi every body:

i have a second order ode and will convert to two ode of first order with maple,how do this work???

eq := diff(y(x), x, x)+2*y(x)+y(x)^2 = 0

## Events in dsolve...

Hi

I  have a system of second order differential equation to be solved numerically. I would like to set up events to halt integration  to find the values of phi when r(phi)=2/3 . Here is my code

DE:=diff(1/r(phi),phi,phi)+(1/r(phi))=(G*M/h^2)+(3*G*M/c^2*r(phi)^2));

ics:=r(0)=2/3,D(r)(0)=0;G:=1;M:=1;h:=1;c:=1;

p:=dsolve({DE,ics},numeric,events=[[r(phi),r(phi),halt]],[diff(r(phi),phi)=0,halt]]);

The code only works for the second event so it halts for r(phi)=1.63... etc

How do i stop this?

Thanks for any help.

## 2nd Order differential equation...

Hey all new to Maplesoft my question is this;

## Second degree proc...

`> seconddegree:= proc(a,b,c) `
` if a=0 then if b=0 and c=0 then print ('infinite solutions')  `
`elif b=0 and c<>0 then print ('impossible')  `
`elif b<>0 and c<>0 then print (' one solution',x=-(c)/(b))fi;   `
`delta:=b^(2)-4 *a*c;    `
`elif if delta=0 then print('double solution',x=-b/(2 a))  `
`elif delta >0 then print ('exist two  solutions',x1=((-b+sqrt(delta...`

## Differentiation formula for parametric equations s...

Hi,    I have the following

for i from 1 to 100 do    x[i]:=cos(θ[i]);     y[i]:=sin(θ[i])  end do;

Now I want to find the first and second derivatives for x[i] and y[i] which are

for i from 1 to 100 do     x1dot[i]:=-sin(θ[i]);     y1dot[i]:=cos(θ[i]);

...